In great tradition of Sybila seminars, I will be talking about reachability in dynamical systems

(fall'14, fall'15, fall'16, fall'17, spring'19)

So, where are we now?

Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes (CAV'18)

Hong, Bartocci, Henzinger

Semialgebraic Dynamical Systems

(bonus points if you already remember what semialgebraic means!)

Safety/Reachability in semialgebraic systems:​

• Invariants or barrier certificates
• Abstraction and hybridisation
• SMT and delta-SMT
• Flowpipe construction (Interval arithmetic, Taylor models)

Piecewise Barrier Tubes: Motivation and Intuition

Combine flow-pipes with barrier certificates

Segment Enclosure Box

Limit your expectations,

one simulation at a time...

Barrier Tube

I life gives you lemons, make a lemonade.

If life gives you an enclosure box, exit plane and list of candidate polynomials, make a barrier certificate.

Experiments